# Probability Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Probability Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. If two dice are thrown, then find the probability of getting the total of $$10$$?

1. $$\frac{1}{15}$$
2. $$\frac{1}{13}$$
3. $$\frac{1}{14}$$
4. $$\frac{1}{12}$$

Answer: (d) $$\frac{1}{12}$$

Solution: number of possible outcomes = $$6 \times 6$$ = $$36$$

number of favourable events = $$\{(4, \ 6), \ (5, \ 5), \ (6, \ 4)\}$$

number of favourable outcomes = $$3$$, then $$Probability = \frac{3}{36}$$ $$= \frac{1}{12}$$

1. Two balls are to be drawn from a box containing $$10$$ blue and $$20$$ red balls. Find the probability of getting that one ball is blue and one ball is red?

1. $$\frac{45}{32}$$
2. $$\frac{40}{87}$$
3. $$\frac{36}{57}$$
4. $$\frac{40}{97}$$

Answer: (b) $$\frac{40}{87}$$

Solution: number of blue balls = $$10$$

number of red balls = $$20$$, then $$Probability = \frac{^{10}C_1 \times ^{20}C_1}{^{30}C_2}$$ $$= \frac{10 \times 20}{435} = \frac{40}{87}$$

1. If two coins are tossed, then find the probability of getting atleast one tail?

1. $$\frac{3}{4}$$
2. $$\frac{4}{3}$$
3. $$\frac{2}{3}$$
4. $$\frac{3}{2}$$

Answer: (a) $$\frac{3}{4}$$

Solution: sample space = $$\{HH, \ HT, \ TH, \ TT\}$$

number of possible outcomes = $$4$$

number of favourable outcomes = $$3$$, then $$Probability = \frac{3}{4}$$

1. From a pack of $$52$$ playing cards, three cards are drawn at random. what is the chance of getting two king and one queen?

1. $$\frac{3}{5225}$$
2. $$\frac{3}{2552}$$
3. $$\frac{3}{5525}$$
4. $$\frac{3}{5552}$$

Answer: (c) $$\frac{3}{5525}$$

Solution: total number of cards = $$52$$

number of cards of king = $$4$$

number of cards of queen = $$4$$, then $$Probability = \frac{^4C_2 \times ^4C_1}{^{52}C_3}$$ $$= \frac{6 \times 4}{44200}$$ $$= \frac{3}{5525}$$

1. A bag contains $$7$$ pink and $$9$$ green balls, if four balls are picked at random then find the probability of getting $$2$$ pink and $$2$$ green balls?

1. $$\frac{9}{120}$$
2. $$\frac{5}{121}$$
3. $$\frac{9}{130}$$
4. $$\frac{6}{113}$$

Answer: (c) $$\frac{9}{130}$$

Solution: number of pink balls = $$7$$

number of green balls = $$9$$, then $$Probability = \frac{^7C_2 \times ^9C_2}{^{16}C_4}$$ $$= \frac{21 \times 36}{10920} = \frac{9}{130}$$

1. A container contains $$20$$ red and $$30$$ blue balls. Find the probability of getting one red ball?

1. $$\frac{2}{3}$$
2. $$\frac{3}{2}$$
3. $$\frac{4}{5}$$
4. $$\frac{2}{5}$$

Answer: (d) $$\frac{2}{5}$$

Solution: number of red balls = $$20$$

number of blue balls = $$30$$, then $$Probability = \frac{^{20}C_1}{^{50}C_1}$$ $$= \frac{20}{50} = \frac{2}{5}$$

1. A box contains three red, six pink and seven black balls. If three balls are picked at random, then find the probability of getting three different colour balls?

1. $$\frac{7}{60}$$
2. $$\frac{9}{80}$$
3. $$\frac{7}{80}$$
4. $$\frac{9}{70}$$

Answer: (b) $$\frac{9}{80}$$

Solution: number of red colour balls = $$3$$

number of pink colour balls = $$6$$

number of black colour balls = $$7$$

then probability of getting three different colour balls, $$Probability = \frac{^3C_1 \times ^6C_1 \times ^7C_1}{^{16}C_3}$$ $$= \frac{3 \times 6 \times 7}{1120}$$ $$= \frac{9}{80}$$

1. There are two boxes, first one contains $$10$$ black, $$20$$ white balls and second one contains $$5$$ black, $$7$$ white balls. If one ball is drawn from each box, then find the probability of getting two black balls?

1. $$\frac{5}{36}$$
2. $$\frac{5}{32}$$
3. $$\frac{7}{36}$$
4. $$\frac{7}{32}$$

Answer: (a) $$\frac{5}{36}$$

Solution: first box contains $$10$$ black and $$20$$ white balls and

second box contains $$5$$ black and $$7$$ white balls

then probability of getting two black colour balls, $$P = \frac{10}{30} \times \frac{5}{12}$$ $$= \frac{5}{36}$$

1. If a fair dice is thrown, then find the probability of getting a number greater than one?

1. $$\frac{4}{5}$$
2. $$\frac{5}{6}$$
3. $$\frac{3}{7}$$
4. $$\frac{4}{7}$$

Answer: (b) $$\frac{5}{6}$$

Solution: number of possible outcomes = $$6$$

number of favourable events = $$\{2, \ 3, \ 4, \ 5, \ 6\}$$

number of favourable outcomes = $$5$$, then $$Probability = \frac{5}{6}$$

1. From a pack of $$52$$ playing cards, two cards are drawn at random. What is the probability of drawing a card of red colour?

1. $$\frac{1}{2}$$
2. $$\frac{1}{3}$$
3. $$\frac{1}{4}$$
4. $$\frac{1}{5}$$

Answer: (a) $$\frac{1}{2}$$

Solution: total number of cards = $$52$$

total number of red colour cards = $$26$$, then $$Probability = \frac{26}{52}$$ $$= \frac{1}{2}$$